[sdiy] A question about Chorus

[rsdio at sounds.wa.com]

This is a great topic.

I've never really thought of it in terms of FM, but a modulated delay  
such as a chorus is similar.

FM, ring modulation, and sampling are all fundamentally the same  
process. Each replaces the original frequencies with their sum and  
difference frequencies. With simple sine waves on input, you only  
have two frequencies, A and B, on input and two new frequencies, A+B  
and A-B, on output. Replacing either sine wave, or both, with a more  
complex signal adds more frequencies. Sampling is the product of a  
square wave modulation and a general audio signal, although we  
generally want to avoid aliasing and thus the audio signal is band- 
limited to be entirely below the Nyquist frequency, and the output is  
also band-limited. But it's basically the same thing. Note that the  
infinite harmonics of the ideal square wave mean that sampled audio  
has an infinite number of aliases, unless filtered.

A modulated delay line shifts the pitch of the original so that the  
output is slightly above or slightly below the input. The original  
frequencies are not present in the output of the BBD, but there is a  
mixing circuit to combine the original with the shifted frequencies  
to allow for detuning and phasing.

Tom mentioned that he wanted to ignore the fact that the chorus is a  
sampled system, but I don't think it's possible to dismiss that. If  
you want to use a BBD with modulation to achieve FM type signals,  
then you'll run into the aliasing of the sampled system very quickly.  
It might be possible to increase the sample rate, which will also  
reduce the delay, and minimize the bandwidth limitations, but I  
believe that a BBD can only run so fast due to the switching speed of  
the FETs.

For an analog system, I'd think that Ring Modulation would be an  
easier way to get FM-type sounds than using an analog BBD delay line  
with a modulated sample clock. You might need some log-linear  
conversion in there somewhere.

Brian Willoughby
Sound Consulting

p.s. Ever notice that badly aliased audio sounds like its ring- 
modulated? That's because it's the same thing.